Heat 2 tablespoons oil in a large nonstick skillet over medium heat. Add sliced garlic; cook, stirring often, until golden brown, about 5 minutes. Remove from heat; using a slotted spoon, transfer the garlic to a paper towel–lined plate. Reserve the oil in the pan.

Add 2 tablespoons butter to the oil in the pan; swirl over medium-high heat until melted. Add 12 ounces gnocchi; cook, stirring and tossing occasionally, until golden brown and crisp, 8 to 10 minutes. Spoon into a medium bowl. Reserve the oil in the pan.

Add 1 (5-ounce) package baby spinach and the chopped artichoke hearts to the pan; cook over medium heat, stirring and folding until the spinach has just wilted, about 2 minutes. Return the gnocchi to the pan; stir to combine.

Remove from heat; add ½ cup heavy cream and ¼ cup feta. Stir until incorporated and creamy, about 1 minute. Add 2 tablespoons lemon juice and 1 teaspoon Italian seasoning; stir to combine. Top with 1 tablespoon chives, the remaining ¼ cup feta and the reserved crispy garlic.